Computing semiparametric bounds on the expected payments of insurance instruments via column generation

TL;DR

This paper introduces a column generation method to efficiently compute semiparametric bounds on insurance instrument payoffs, accommodating additional distributional information and improving practical applicability over previous semidefinite programming approaches.

Contribution

It presents a novel column generation approach for univariate semiparametric bounds, enabling the inclusion of extra distributional constraints and simpler worst-case distribution construction.

Findings

Practical linear programming solutions for bounds

Inclusion of unimodality and continuity constraints

Efficient computation of worst-case distributions

Abstract

It has been recently shown that numerical semiparametric bounds on the expected payoff of fi- nancial or actuarial instruments can be computed using semidefinite programming. However, this approach has practical limitations. Here we use column generation, a classical optimization technique, to address these limitations. From column generation, it follows that practical univari- ate semiparametric bounds can be found by solving a series of linear programs. In addition to moment information, the column generation approach allows the inclusion of extra information about the random variable; for instance, unimodality and continuity, as well as the construction of corresponding worst/best-case distributions in a simple way.